Dear All,
Please join the Department of Applied Mathematics for the following
colloquium:
Wednesday, December 1, 4:40pm, E1 106
Samuel Drapeau
Department of Mathematics
Humboldt University - Berlin
Title: Risk Preferences and their Robust Representation: Beyond random
variables, a setup independent approach
Abstract: Due to the plurality of interpretations of risk, we concentrate on
context invariant features related to this notion: diversification and
monotonicity. We introduce and study the general properties of three key
concepts in an abstract framework: risk order, risk measure and risk
acceptance family. Our main result is a uniquely characterized robust
representation of lower semi-continuous risk orders.
We will also give some new results when monotonicity actually ensures the
lower semicontinuity of risk orders.
This general approach to risk perception leaves room for different
interpretations of risk perception within one concept depending on the
setting and one's perspective.
We illustrate this with several settings.
In the setup of random variables, where risk perception can be interpreted
as a model risk, we give a robust representation for numerous risk measures:
various certainty equivalents, or a general version of Aumann and Serrano's
economic index of riskiness among others.
In the setup of lotteries where risk perception can be seen as a
distributional risk, we show that the Value at Risk is a risk measure on
this level (not for random variables) and provide a robust representation
for it. In the setup of consumption patterns where risk perception is
related to a discounting risk, we provide a robust representation of
intertemporal risk measures \`a la Hindy, Huang and Kreps or Epstein and
Zin.
We finally discuss in the setting of state dependent lotteries à la Anscombe
and Aumann, the interplay between model risk and distributional risk.
Best regards,
Igor Cialenco
-------------------------------------------------
Illinois Institute of Technology
Department of Applied Mathematics
10 W 32nd Str, E1 234C
Chicago, IL 60616
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